Abstract

The exploration of Mesopotamian mathematics took its beginning together with thedecipherment of the cuneiform script around 1850. Until the 1920s, “mathematics in use” (number systems, metrology, tables and some practical calculations of areas) was the object of study – only very few texts dealing with more advanced matters were approached before 1929, and with quite limited results. That this situation changed was due to Otto Neugebauer – but even his first steps in 1927–28 were in the prevailing style of the epoch, so to speak “pre-Neugebauer”. They can be seen, however, to have pushed him toward the three initiatives which opened the “Neugebauer era” in 1929: The launching of Quellen und Studien, the organization of a seminar for the study of Babylonian mathematics, and the start of the work on the Mathematische Keilschrift-Texte. After a couple of years François Thureau-Dangin (since the late 1890s the leading figure in the exploration of basic mathematics) joined in. At first Thureau-Dangin supposed Neugebauer to take care of mathematical substance, and he himself to cover the philology of the matter. Very soon, however, both were engaged in substance as well as philology, working in competitive parallel until both stopped this work in 1937–38. Neugebauer then turned to astronomy, while Thureau-Dangin, apart from continuing with other Assyriological matters, undertook to draw the consequences of what was now known about Babylonian mathematics for the history of mathematics in general.

487

Jens Høyrup

Archimedes: Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance

Abstract

With only Apuleius and Augustine as partial exceptions, Latin Antiquity did not know Archimedes as a mathematician but only as an ingenious engineer and astronomer, serving his city and killed by fatal distraction when in the end it was taken by ruse. The Latin Middle Ages forgot even much of that, and when Archimedean mathematics was translated in the 12th and 13th centuries, almost no integration with the traditional image of the person took place. With the exception of Petrarca, who knew the civically useful engineer and the astrologer (!), fourteenth-century Humanists show no interest in Archimedes. In the 15th century, however, “higher artisans” with Humanist connections or education took interest in Archimedes the technician and started identifying with him. In mid-century, a new translation of most works from the Greek was made by Jacopo remonensis, and Regiomontanus and a few other mathematicians began resurrecting the image of the geometer, yet without emulating him in their own work. Giorgio Valla’s posthumous De expetendis et fugiendis rebus from 1501 marks a watershed. Valla drew knowledge of the person as well as his works from Proclus and Pappus, thus integrating the two. Over the century, a number of editions also appeared, the editio princeps in 1544, and mathematical work following in the footsteps of Archimedes was made by Maurolico, Commandino and others. The Northern Renaissance only discovered Archimedes in the 1530s, and for long only superficially. The first to express a (purely ideological) high appreciation is Ramus in 1569, and the first to make creative use of his mathematics was Viète in the 1590s.

Abstract

The Yiji jing 易筋經 (The Canon for Supple Sinews) of 1624 describes martial training currently practiced, particularly in Chinese communities. This article compares two forms that the two co-authors learnt in different places: Singapore and Kunming in the People's Republic of China. One form is known as the Hong Fist (hongguan洪拳) version of the Yijin jing, the other was taught as a form of qigong 氣功. This article focuses on the training of the authors in their respective practice. It demonstrates that the techniques learned instilled in the authors an attentiveness to the meanings that shaped their practice. These meanings were not primarily comprehended in a cognitive fashion but felt and experienced. In particular, the materiality of the environment, or more precisely the resistances that the environment posed to a practitioner, appear to have shaped the practice of the Yijin jing in distinctive ways. As argued here, the practitioners enskilled themselves through their practices into a world of either jin筋/勁 (sinew/power) or qi 氣 (breath/wind).

Abstract

Peter Fulde is not only one of Germany’s leading solid-state physicists but is prominent also due to his outstanding career, his general involvement in science, and the exceptional activities he undertook in organizing science in various circumstances. Fulde grew up in the eastern part of the country and went to the West as a student. He obtained his PhD in the United States and then returned to Germany to become full professor at the University of Frankfurt at the age of 32 and later director in various research institutes. He was a member of the German Science Council (Wissenschaftsrat), the board of the German Physical Society (DPG) and numerous other bodies. After the re-unification of Germany he returned to the East and built up the Max Planck Institute for the Physics of Complex Systems in Dresden. Finally, after his retirement in 2007, he followed a call to South Korea to head a similar institute there and eventually helped to establish a Korean analogue of the German Max Planck Society. The interview presented here follows the steps of his life. It was conducted on the occasion of his 80th birthday in April of 2016 and is supplemented by a curriculum vitae and by two brief accounts of his physics research and of his role in Dresden and Korea in the context of the Max Planck Society.

Abstract

There are powerful social, political, and epistemological reasons for concealing (or revealing) certain people and practices in the course of scientific research and publication. The human sciences—including biology and biomedicine as well as anthropology, linguistics, and social science—depend upon people with diverse values and expertise, who have varied motivations and degrees of political agency. Research encounters are often orchestrated by actors behind the scenes—tissue donors, survey respondents, student subjects, translators, activists, ethics review boards, civic or religious institutions, lawyers, nurses, and archivists. Their contributions move in and out of the shadows as scientific knowledge is made, with important consequences for the authority and authenticity of research findings. Through a collection of case studies, this volume encourages methodological reflection on whether and how historians of science and STS scholars might recover contributions to the human sciences. Ultimately the volume asks how our professional, institutional, geographical and political circumstances condition whom we claim to speak of and for.

Abstract

Around 1801 Louis-Bernard Guyton de Morveau (1737–1816) designed his famous fumigating machine. The machine spread a controlled emission of a specific gas—described as an oxygenated acid—that was supposed to destroy the contagious miasmas in the air, objects, and bodies. During the 1804 outburst of the yellow fever, the Spanish Government ordered that the original design of Guyton’s fumigating machine be adapted to the Spanish market for extensive use in households. This was done against some criticism, as the nature of the contagion was avowedly unknown and the acid fumigation technology polemic. Nonetheless, the machine was pictured as crucial for the health of individuals and for society as a whole.
The essay looks at the fumigating machine as a way of exploring how scientific and political practices pervaded societies and, vice-versa, how ways of interpreting nature and politics became embedded in artifacts. It will show, first, how the machine served to spread the new French chemistry among Spaniards; second, how it embodied a new relationship between the citizens and the state, and third, how this artefact was imported by the Spanish absolutist state, appropriated, and used for political propaganda. By focusing on a chemical artefact, it shows a historically complex and significant interweaving of theory, material culture, and politics.

482

Wolfgang Gebhardt

Erich Kretschmann. The Life of a Theoretical Physicist in Difficult Times

Abstract

Erich Kretschmann (1887–1973) was a German theoretical physicist whose work on Einstein’s General Theory of Relativity (1917) offered some interesting insights, but was also critical of Einstein’s semantics. Einstein responded in a paper in 1918 and agreed that Kretschmann’s criticism was valid. Kretschmann wrote his thesis under the supervision of Max Planck and obtained his doctorate in 1914. A psychiatric disease during his adolescence
made him permanently unfit for military service and saved him from having to participate in the First World War. From 1920 he lectured in theoretical physics at the University of Königsberg. In 1926 he became an apl. professor, a position which he held until 1945. After his escape from Königsberg in January 1945 he found temporary accommodation at Rendsburg, Schleswig-Holstein. In 1946 he was appointed as a full professor of theoretical physics at the Martin-Luther-Universität Halle.

Abstract

Since its development in economic history, the notion of ‘Useful Knowledge’ has found wide resonance in very diverse fields, engaging scholars working on codified knowledge and scientific practices, material culture and technological innovation, experimentation and policy issues. This preprint presents some of the contributions on this theme delivered at the workshop ‘The Making of Useful Knowledge’ (MPIWG Berlin, 30–31 October 2014).
The meeting aimed at problematizing the apparently coherent picture of useful knowledge that has arisen out of the works of economic historians like Joel Mokyr, and at testing and evaluating the employment of notions of usefulness in the longue durée, moving away from a specific focus on pre-industrial economic growth. Because of this diachronic approach, case studies spanned from the early modern period to the twentieth century.
This volume collects an introduction and six essays by Karel Davids, Jonathan Harwood, Ursula Klein, Thomas Morel, Giuditta Parolini and Cesare Pastorino. Topics of these contributions range from commercial accounting, plant breeding and maritime technology, to mining, mineralogy and applied statistics. The workshop ‘The Making of Useful Knowledge’ was organized by Thomas Morel, Giuditta Parolini and Cesare Pastorino as part of the activities of the Berlin Center for the History of Knowledge.

Abstract

This paper is the translation by Giampiero Esposito of a paper originally published in French in Acta Mathematica 88, 141-225 (1952) under the title: Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. The first three chapters are devoted to the solution of the Cauchy problem, in the nonanalytic case, for a system of nonlinear second-order hyperbolic partial differential equations with n unknown
functions and four independent variables. This task is accomplished in chapter III by using the system of integral equations fulfilled by the solutions of partial differential equations that approximate the original nonlinear system. In chapter IV, such results are applied to the vacuum Einstein equations. The resulting Ricci-flatness condition is expressed, in isothermal coordinates, through nonlinear equations of the kind studied here. It is hence proved that the solution of the Cauchy problem, pertaining to such nonlinear equations, satisfies over the whole of its existence domain the isothermal conditions if the same is true for the initial data. One therefore obtains a solution of the vacuum Einstein equations which is unique up to a coordinate change.

Abstract

When the Federation of German Scientists (VDW) was founded as the West German section of Pugwash in the late 1950s, several high-profile scientists from the Max Planck Society (MPG), especially nuclear physicists, were involved. Well into the 1980s, institutional links existed between the MPG, the Federal Republic’s most distinguished scientific research institution, and Pugwash, the transnational peace activist network that was set up in 1957 in the eponymous Nova Scotia village following the Russell-Einstein Manifesto. In the beginning, the two organisations’ relationship was maintained primarily by the physicist and philosopher Carl Friedrich von Weizsäcker. However, it was difficult right from the start, and the distance between them grew during the rise of détente in the 1970s, when the scientific flagship MPG was deployed more and more frequently in matters of foreign cultural policy, not only for the FRG but for the western alliance as a whole. This contribution explores the resources and the risks of transnational political engagement – not only as the individual strategies of top-ranking researchers, but also in terms of policy deliberations within a leading scientific organization at one of the Cold War’s sharpest divisions: the front line between two Germanys.

478

Alexander Blum, Jürgen Renn, Matthias Schemmel

Experience and Representation in Modern Physics: The Reshaping of Space

Abstract

The paper discusses the interplay of experience and representation in disciplinarily structured science using the example of the fundamental changes in the concepts of space and time brought about by the advanced formalism of twentieth-century physics, which enabled the integration of a growing corpus of experiential knowledge. In particular the question of why certain parts of experiential knowledge had an impact on concepts of space and time, while other parts did not have such an impact, is addressed.

Abstract

We investigate possible tools and approaches to develop a Digital Scrapbook, a virtual research environment inspired by the recursive nature of research for scholars where they can combine web and own resources into a new scholarly edition readily enabled for Open Access. Web resources are interlinked in the digital scrapbook by content capture and detail selection, rather than sole bookmark or link to resource URL, along with necessary accompanying metadata. We analyse several open source and commercial tools, with special focus on a Scrapbook-X Firefox Add-On, in order to match to desired Digital Scrapbook features. We further address the wider requirement context for development of such Digital Scrapbook environment, discussing both technical and user experience dimensions. We conclude with a recommendation on how to approach the development and operation of a Digital Scrapbook environment.

Abstract

We investigate possible tools and approaches to develop a Digital Scrapbook, a virtual research environment inspired by the recursive nature of research for scholars where they can combine web and own resources into a new scholarly edition readily enabled for Open Access. Web resources are interlinked in the digital scrapbook by content capture and detail selection, rather than sole bookmark or link to resource URL, along with necessary accompanying metadata. We analyse several open source and commercial tools, with special focus on a Scrapbook-X Firefox Add-On, in order to match to desired Digital Scrapbook features. We further address the wider requirement context for development of such Digital Scrapbook environment, discussing both technical and user experience dimensions. We conclude with a recommendation on how to approach the development and operation of a Digital Scrapbook environment.

Abstract

The subject of this essay concerns the role of chemistry during the Industrial Revolution in Britain, and as such its focus is upon“practical“ or “applied“ chemistry and its functional development within the rapidly industrializing circumstances of the town of Glasgow in the later 18th. and 19th. centuries.The earlier part of this period also witnessed the decades of the so-called Chemical Revolution, the developments in chemical science associated with Antoine Lavoisier and his French colleagues, initiated in the 1770’s and gaining increasing acceptance from the mid-1780’s onwards.
One theme of the essay is thus the form of relations holding between these “Two Revolutions“. Were the advances in practical, industrial chemistry significantly derived from the new chemistry, and how, more generally, may such technical innovations be historically understood.? A second theme concerns the variety of locations and forms of industrialized chemical production which characterize the period in question, and a third is the diverse nature of chemical entrepreneurship exhibited by Glasgow’s pre-eminent chemical industrialists.
Close attention is paid throughout to the chemical, industrial and social characteristics of specific Glaswegian sites, such as Tennant & Co.’s St. Rollox Works and the Macintosh family’s Dunchatton Cudbear Works. The presence of Glasgow’s commercial and educational institutions is also emphasized as significantly relevant for the social and intellectual formation of what became, by 1800, the first generation of industrial chemists in Glasgow. The essay concludes with further reflection upon the historiographical complexities attending our attempts to grasp the nature of economic, technical and scientific change during this revolutionary period.

Abstract

The two papers in this preprint provide a framework for analyzing the history of knowledge from the perspective of extended evolution, a conceptual framework that analyzes evolutionary processes as transformations of extended regulatory network structures and is designed to apply to a whole range of phenomena, from genome and biological to cultural and technological evolution. All of these phenomena can be seen as a form of extended knowledge evolution.

Abstract

This article summarizes a historical perspective on the nation’s experience in the development of nuclear physics, with a special emphasis on its relationship with the Cuban Nuclear Program and the scientific and technological achievements attained as well as their social and economic impact. The development of nuclear energy and nuclear facilities requires the creation of specialized institutions, the training of professionals in the field, the structuring of interdisciplinary groups made up of nuclear physicists and specialists in theoretical and experimental physics, and engineers and specialists in other areas. This article also addresses the multiple peaceful applications introduced in Cuba, particularly those related to the scientific nuclear program.

469

Dominic Olariu

The Misfortune of Philippus de Lignamine’s Herbal or New Research Perspectives in Herbal Illustrations From an Iconological Point of View

Abstract

The essay focuses on of the very first incunabulum herbal, printed in Rome by Philippus de Lignamine in 1482/83. It takes this incunabulum as a starting point for further reflections on the status of plant illustrations and their naturalism in herbals of the 15th and 16th centuries. Philippus’ intention was to edit a herbal of the so-called Pseudo-Apuleius tradition. For this, he used the schematized illustrations of a Pseudo-Apuleius manuscript he had previously discovered as patterns for the plant illustrations of his print. Philippus believed the manuscript to be a Roman antique herbal manuscript, but investigations by Hunger (1935) have shown that the manuscript was a ninth-century Pseudo-Apuleius copy. The essay asks for the reason of Philippus’ reuse of schematic plant pictures. It argues that at the end of the 15th century, the belief in the truthfulness of antique herbal texts was still as big as to stimulate Philippus to copy the presumed antique illustrations. There was an intense printing activity of treatises completely or partly dedicated to herbs during the last quarter of the 15th century, in Germany as well as in Italy. At the same time, however, herbal illustrations in manuscripts, during the last third of the 15th and the first third of the 16th century, were becoming far more naturalistic than prints and employed own means of picturing plants. The manuscripts also used pictorial patterns, but were more inventive in iconography during the first third of the 16th century, employing nature prints and dried plants, and therefore employed their own ways to convey knowledge on plants.

468

William G. Boltz and Matthias Schemmel

Theoretical Reflections on Elementary Actions and Instrumental Practices: The Example of the Mohist Canon (TOPOI – Towards a Historical Epistemology of Space)

Abstract

The paper discusses sections of the so-called ‘Mohist Canon’, an ancient Chinese text from about 300 BCE, that are related to concepts of space, time, matter, and motion. It is argued that the text documents theoretical reflections on the linguistic representations of non-theoretical forms of knowledge such as knowledge universally attained in ontogenesis and knowledge attained by employing culture-specific instruments or practices. Finally, the case of the ‘Mohist Canon’ is compared to parallel cases of theoretical reflection documented in Greek antiquity, identifying similarities and differences between the two traditions, and addressing the question of possible explanations for these similarities and differences.

467

Carl H. Meyer & Günter Schwarz

The Theory of Nuclear Explosives That Heisenberg Did not Present to the German Military

Abstract

There has been much speculation about what role the leading German physicist of the Nazi era, the prodigious Werner Heisenberg (1901–1976), played in the failure of Nazi Germany to pursue development of an atomic bomb. Reading extreme views of Heisenberg that appeared in the literature piqued our curiosity, and we analyzed Heisenberg’s 1939/40 report to German Army Ordnance hoping to establish additional facts that would throw light on this controversy.
When we read Heisenberg's 1939/40 report, we saw that while it contained many equations that related to the development of a nuclear reactor, it had no mathematical/scientific derivations related to the development of an atomic bomb, although, as we show in this paper, it would have been easy for Heisenberg to develop and supply such information. He actually did it quickly while interned in the U.K., at Farm Hall after the war in Europe ended, incorporating the theory and its implications in his August 14, 1945, lecture.
Nevertheless, despite the fact that Heisenberg did not develop a theory of nuclear explosives, he should have been able to deduce the critical radius (mass) formula for an atomic bomb from information contained, although somewhat scattered, in his 1939/40 report in which he only developed a theory about the workings of nuclear reactors. Not only that, but an estimate of the critical mass, although a crude one along the lines Frisch and Peierls pursued, could also have been obtained that would have suggested that building a nuclear explosive might be feasible. Heisenberg, whose intuition was legendary, should certainly have been able to build on his work on the theory of nuclear reactors to take the steps needed to extend that theory to a nuclear explosive.
We address also the apparent discrepancy between the above statement and Heisenberg's references to “tons” when he spoke of the critical mass at Farm Hall and Heisenberg's short-cut formula that he used in his Farm Hall lecture on August 14, 1945, without any explanation.

Abstract

Starting from the assumption that Ptolemy worked with a value for the circumference of the Earth that was much too small, his coordinates may be recalculated for the circumference measured by Eratosthenes, using spherical trigonometry (see Preprint 464). Such recalculations, for which localities within one region must always be related to at least one reference point, may help to discover inconsistencies in former attempts at systems of identification and to put forward new hypothesis and assess their plausibility. In this article, this approach is applied to the region of the Tarim Basin. As one of the results, a whole water system described in Ptolemy, whose identification posed notorious problems in the history of the interpretation of Ptolemy’s data, can in fact be identified as a duplicate of another such system.

464

Irina Tupikova

Ptolemy’s Circumference of the Earth (TOPOI – Towards a Historical Epistemology of Space)

Abstract

The relationship between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography is discussed. A simple transformation of the Ptolemaic coordinates to the circumference of the Earth measured by Eratosthenes, based on the assumption that the metrical values of the stadion used by both Ptolemy and Eratosthenes are equivalent, drastically improves the positions of the locations given in Ptolemy’s catalogue at least for a great part of the oikoumenē. Comparing the recalculated positions of the identified localities with their actual positions, it turns out that the distances extracted by Ptolemy from ancient sources are remarkably precise. This in turn confirms the high precision of Eratosthenes’s result for the circumference of the Earth. It is shown that many distortions of Ptolemy’s world map can be explained as pure mathematical consequences of a mapping onto the surface of a sphere of wrong size. Keywords: Ancient Geography, Ptolemy, Eratosthenes

Abstract

Post-revolutionary Cuba is a unique case among underdeveloped countries. This small plot of land – less than one thousand of the emerged Earth surface with barely 1.5 per thousand of the World population, with scarce resources – decided in 1959 to develop an advanced scientific system, with the explicit goal of both solving the most urgent problems for the development of the country and for its population (primarily the health problems), and to overcome the condition of subalternity. This process was very original also for the free and open-minded recourse to every kind of support and collaboration, with Soviet and Western scientists and institution, besides a typical Cuban inventiveness. The success of this project was striking. In the following three decades Cuba built an advanced and articulated scientific system, and achieved an excellence level in leading scientific fields. Among these, one can mention electronics and superconductivity, but probably the most striking top-level results were achieved, quite surprisingly, in a capital-intensive and typically American field like biotechnology. This last success has called the attention of the most qualified international Journals, such as Nature, Science and the specialized literature. Even more remarkable is that the development of Cuban biotechnology was completely independent from any collaboration and support from the Soviet Union, which was backward in this field.
At the turn of the 1980s, however, the collapse of the Soviet Union left Cuba in an extremely difficult economic situation, seriously putting at risk the achievements of the Revolution, and posing again the threat of subalternity. Most analysts even predicted the downfall of the Cuban economy and regime. The American embargo was intentionally worsened. Actually, the Cuban scientific system withstood the tremendous shock despite the loss of every support, confirming the maturity and autonomy it had attained, even though the economic difficulties inevitably undermined many scientific sectors. In face of such a critical situation, the Cuban government reconfirmed and reinforced the choice of supporting its most advanced and profitable scientific sectors, especially in the biomedical sector, as a strategy to overcome the present difficulties. This strategy proved to be once again a well chosen choice.
The present essay presents a wide-ranging reconstruction of the complex process of Cuban scientific development, based on, and reviewing the relevant literature that has addressed this problem. The explicit thesis is that the Cuban way of addressing and overcoming subalternity is unique in contemporary history.
An original contribution is the first reconstruction of the unique role of Italian biologists in the training and growth of Cuban geneticists and biotechnologists between mid 1960s and mid 1970s.

460

Stefano Bordoni

Unexpected Convergence between Science and Philosophy: A debate on determinism in France around 1880

Abstract

In 1878 the mathematician Joseph Boussinesq pointed out a structural analogy between some features of living beings and singular solutions of differential equations. Sudden transitions between ordinary and singular solutions could represent sudden release of energy in biological process and in the fulfilment of free will. He assumed that a guiding principle rather than a physical action might lead the system beyond the threshold of singular points. Deterministic processes, which corresponded to ordinary solutions, gave way to indeterministic processes, which corresponded to singular solutions. Alongside the mathematical pathway, a different conceptual stream had already emerged in the second half of the nineteenth century. Both physicists and physiologists made use of concepts like triggering actions and guiding principles in order to represent explosions and unstable equilibrium in inanimate matter, and the complex interaction between volitions and motions in human beings. A third conceptual stream was represented by philosophical debates on the problematic link between deterministic physical laws and free will. The new issues stemming from the fields of mathematics, physics, and life sciences found room in philosophical journals, but the interest of philosophers gradually faded away towards the late 1880s. At the same time, the majority of mathematicians and physicists had never shown a systematic interest in this subject matter. We find in Boussinesq an original and almost isolated attempt to merge mathematical, physical, biological issues into a consistent philosophical framework. However questionable his research programme might be, it was actually a daring and systematic one. In the twenty-first century, some philosophers of science rediscovered the problematic link between determinism and singular solutions of differential equations. The memory of late nineteenth-century debates had already disappeared, but recently Marij van Strien has put forward a direct comparison between those debates and recent theses on determinism.

Abstract

A debate which traverses much of the scientific literature in the Renaissance is connected to the problem of the relative greater “size” of earth or water and their reciprocal disposition. Stimulated by the great geographical discoveries of the time, intellectuals had to find new solutions to the old problem inherited from Aristotelian physics about how it was possible that an habitable land could emerge, when the natural weight of the earth would supposedly submerge it fully below the sphere of water.
The examination of some significant texts of Alessandro Piccolomini, Antonio Berga and Giovanni Battista Benedetti documents the emergence of the new, integral concept of “globe” (globus terracqueus), which can be compared to the model of concentric spheres of the elements handed down by the whole Aristotelian tradition – a concept already proposed by Copernicus, but which became increasingly popular in the following decades. According to this new model, water and earth were no longer to be considered like two distinct spheres contained in one another, but rather as two elements which continuously interact with one another within a single sphere, and through a wide range of phenomena such as tides, floods, erosion, landslides, etc..
Accepting this innovation meant not only creating the conditions for the rise of the issue of a “history” of the Earth, but also involved dealing a first blow to the terrestrial physics of Aristotle. This blow was followed a few years later by the observations of Brahe, Kepler and Galileo which cast further doubt on Aristotle’s celestial physics.

Abstract

In discussions of the possible connections between Copernicus and his Islamic predecessors, the so-called Ṭūsī-couple, invented by the 13th-century Persian polymath Naṣīr al-Dīn al-Ṭūsī, has often been invoked by various modern historians to bolster their cases for or against transmission from Islamic astronomy to Copernicus. This paper seeks to clarify the possible routes of transmission by first explaining the various versions of the Ṭūsī-couple that were meant to produce either straight-line or curvilinear oscillations from circular motions, and then summarizing what is known about this transmission, providing new evidence as well as reinterpreting existing evidence. It becomes clear that there are a variety of avenues by which the various couples could have come into Europe, such as through Byzantium, through Spain, and through Italy, and that Copernicus acknowledges the earlier existence of at least one version of the couple in a draft of De Revolutionibus. The paper concludes with a historiographical note that maintains that the long, complex development and use of the Ṭūsī-couples within an Islamic context, and the lack of anything comparable in Europe before Copernicus, provides a compelling argument for transmission rather than parallel discovery within a Latin/European context.

Abstract

To develop a more fine-grained picture of how the theory of general relativity was received and elaborated from 1914 until 1924, we move outside the personal networks of its creator, Albert Einstein. We set aside the question when and why Einstein himself came to recognize that the new field physics required higher mathematics and focus on the cross-fertilization between mathematics and physics that contributed to the theory. The breakdown of disciplinary boundaries had a greater impact on academic politics in Germany, as the intrusion of mathematics heightened tensions that had long been brewing within the German physics community. A second factor contributing to the tensions was the increasing prominence in the community of German physicists of those of Jewish extraction. We examine these phenomena in two localities, Göttingen and Berlin that serve as focal points for polarization in the natural sciences.
First, we discuss the openness in their scientific approach and in their recruitment policy of the paladins of Göttingen—Felix Klein and David Hilbert—and then proceed to trace the fruits of that policy in the successor generation that was largely composed of Jews.
We then look at Einstein in Berlin, and more specifically, at how his “conversion” to Zionism in 1920 crystallized his idiosyncratic views on cultural politics that alienated him from others in the Berlin community, including some of his Jewish colleagues. We examine four incidents that undergird his solidarity with Hilbert, a “Gesinnungsgenosse,” who believed that belonging to the international community of scientists took precedence over any sense of patriotic duty or ethnic identity.

Abstract

Around 1930, it was discovered that certain Babylonian cuneiform texts contain calculations that agree with what turns up in the solution of second-degree equations. Since the meaning of most of the terminology had to be derived from the numbers contained in the texts, this led to a reading of these as numerically based algebra.
This interpretation stood unchallenged until the author of the present book discovered around 1982 that it was incompatible the global structure of the terminology. As it turns out, two different and non-synonymous operations had both been understood as addition; two different subtractive operations had been conflated, and four different operations had been seen as one and the same multiplication. Instead, the structure points to a technique based on a geometry of squares and rectangles with measurable sides and areas.
Avoiding such philological detail as would only be informative for readers that are familiar with basic Assyriology (yet with appendixes meant for these), the book analyses a number of texts in "conformal translation", that is, a translation in which the same Babylonian term is always translated in the same way and, more important, different terms are always translated differently.
All of these texts are from the second half of the Old Babylonian period, that is, 1800-1600 BCE. It is indeed during this period that the "algebraic" discipline, and Babylonian mathematics in general, culminates. Even though a few texts from the late period show some similarities with what comes from the Old Babylonian period, they are but remnants.
Beyond analyzing texts, this preprint gives a general characterization of the kind of mathematics involved, and locates it within the context of the Old Babylonian scribe school and its particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid's geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics.

When Historiography met Epistemology. Duhem’s early philosophy of science in context

2013

Abstract

If the emergence of physics as a definite academic discipline was a heritage of the late nineteenth century, the emergence of a new theoretical practice, and the settlements of chairs of theoretical physics were the most interesting outcome of that process. The hallmark of the new theoretical practice was the awareness that the alliance between the mathematical language and the experimental practice celebrated by Galileo had to be updated. Besides “definite demonstrations” and “sound experiments” there was a third component, which could be labelled conceptual or theoretical: it dealt with principles, models, and patterns of explanation. That conceptual component, neither formal nor empirical, came to be looked upon as a fundamental component of scientific practice. It is worth remarking that, in that fin de siècle, science had finally managed to realize, at least in part, Bacon’s dream, and the myth of scientific progress emerged.
In the debates on science which took place in France from the early 1870s to the early 1890s two main issues were at stake: determinism and reductionism. On the one hand we find some scientists, historians, and philosophers who relied on simplified epistemological and historiographical frameworks, and put forward an optimistic cult of human progress. On the other hand, a sophisticated point of view on science was put forward by scientists and philosophers who did not deny the effectiveness of scientific progress but were able to go beyond the simplified conception of scientific practice as an unproblematic alliance between mathematical and empirical procedures.
In 1892 the young physicist Pierre Duhem published the first paper explicitly devoted to meta-theoretical issues or, to make use of a more recent expression, to philosophy of science. At that time he had already published a book on thermodynamic potentials and their applications to different fields of physical sciences, and a demanding paper, where he had put forward an original mathematical approach to thermodynamics on the track of Analytical Mechanics. Theoretical physics, the history of physics, and meta-theoretical remarks on science were mutually interconnected in Duhem’s actual praxis. The historical and epistemological remarks he began to publish systematically in the 1890s were subsequently collected in the book he published in 1906, La théorie physique, son objet, et sa structure.
He represented the scientific enterprise as a three-stages task: from the knowledge of “specific facts”, the human mind was able to derive some “experimental laws” by induction, and then create a scientific theory. If the objects of experimental laws were facts, the objects of physical theories were experimental laws. In any case, a theory had nothing to do with the truth: it could not be qualified as true or false, but “suitable or unsuitable, good or bad”. The plurality of theoretical frameworks corresponding to a set of laws was consistent with this essential feature of theories. Moreover he put forward three fundamental theses on experimental physics: first, a physical experiment was not a purely empirical process; second, it could not be so powerful as to lead to the refutation of a single hypothesis; third, it was less reliable, even though more precise, than ordinary experience.
After the Second World War some themes which had been put forward in the late XIX-century philosophy of science re-emerged in an unexpected way. In reality, Duhem’s books and papers had almost been forgotten, but a new interest in some of his meta-theoretical theses emerged in the context of a philosophical tradition that was deeply linked to logic. In 1951 Willard van Orman Quine sharply criticised both the dichotomy analytic/synthetic and reductionism, but he neither quoted from nor mentioned Duhem. In 1960 Adolf Grünbaum put forward a refutation of what he called “Duhemian argument”, but the core of Duhem’s meta-theoretical remarks got lost in a net of logical deductions which were extraneous to their context.
Only from the 1970s onwards historians, historians of science, and philosophers of science began to be attracted by late XIX-century context in general, and Duhem’s philosophy of science in particular. Late XIX-century philosophy of science stemmed from a remarkable epistemological and historiographical awareness, and that awareness would deserve to be further explored.

Abstract

The paper reviews Einstein's engagement as a mediator and popularizer of science. It discusses the formative role of popular scientific literature for the young Einstein, showing that not only his broad scientific outlook but also his internationalist political views were shaped by these readings. Then, on the basis of recent detailed studies, Einstein’s travels and their impact on the dissemination of relativity theory are examined. These activities as well as Einstein’s own popular writings are interpreted in the context of his understanding of science as part of human culture.

Abstract

This paper focuses on the linguistic representation of spatial concepts in two unrelated languages with a non-written tradition. It explores the degree to which environmental experience and spatial orientation is reflected in language, i.e., it is in line with anthropological linguistic approaches placing language in its social and cultural context, and its cultural practices. Spatial knowledge is not only encoded in concepts or categories, but is embodied in the lived histories of human beings, and their cultural and linguistic practices. The cultures under survey present an alpine region (Eipo, Papua Province, Indonesia) and vast prairies (Dene Chipewyan, Alberta, Canada). The mental and perceptual course maintaining in these cultures rely on cognitive maps, i.e., the orientation techniques are processes of inference within the structure of cognitive maps. We adopt cognitive maps as known from navigation techniques of dead reckoning of orientation. This kind of navigation is based on dynamic cognitive maps and mental triangulation so that the navigator has a spatial conception of their position at any time. It is argued here that this is of special importance also for orienting oneself in the alpine regions of Eipo or the vast prairies extensions of the Dene.
Our question concerns the relationship between non-linguistic information and spatial language. The point of departure is that non-linguistic information has its impact upon spatial language and categorization, i.e., reference of space and its relation to semiotic systems. We present language data indicating the influence and constructive process of environmental landmarks and cultural heritage upon shaping of spatial categorization in the two languages.

446

Matthias Schemmel

Elements of a Historical Epistemology of Space (TOPOI – Towards a Historical Epistemology of Space)

2013

Abstract

The essay presents an outline of a historical epistemology of space in the sense of a developmental theory of forms of spatial thinking. Starting with the natural conditions of spatial cognition through to concepts of space imposed by advanced disciplinary science, manifestations of spatial thinking in different cultures and historical epochs are sketched. The essay attempts to contribute to an assessment of the epistemic status of human spatial knowledge by highlighting genetic and structural relations between the different forms of knowledge. While the occurrence of each new form depends on specific socio-cultural conditions, its concrete realization does not solely depend on these conditions, but also on the cognitive structures it builds upon and on the further experience made possible by these conditions. Different forms of spatial knowledge do not replace each other in historical succession; they are simultaneously present within single societies and influence each other.

Abstract

From Rudolf Clausius’ classical version of Thermodynamics two different traditions of research really emerged. If James C. Maxwell and Ludwig Boltzmann pursued the integration of thermodynamics with the kinetic theory of gases, others relied on a macroscopic and more abstract approach, which set aside specific mechanical models. Starting from 1869, the French engineer François Massieu was able to demonstrate that thermodynamics could be based on two “characteristic functions” or potentials. Josiah W. Gibbs and Hermann von Helmholtz exploited the structural analogy between Mechanics and Thermodynamics: from a mathematical point of view, Helmholtz’s “free energy” was nothing else but Gibb’s first potential. In the meantime, in 1880, the young German physicist Max Planck aimed at filling the gap between thermodynamics and the theory of elasticity. Five years later Arthur von Oettingen put forward a formal theory, where mechanical work and fluxes of heat represented the starting point of a dual mathematical structure. In 1891 Pierre Duhem generalized the concept of “virtual work” under the action of “external actions” by taking into account both mechanical and thermal actions. Between 1892 and 1894 his design of a generalized Mechanics based on thermodynamics was further developed: ordinary mechanics was looked upon as a specific instance of a more general science.
KEY WORDS: Mechanics, Thermodynamics, Potentials, Work, Heat, Energy, Lagrange’s equations, General equations.

442

William G. Boltz and Matthias Schemmel

The Language of ‘Knowledge’ and ‘Space’ in the Later Mohist Canon (TOPOI – Towards a Historical Epistemology of Space)

Abstract

The paper presents translations and interpretations of numerous sections from the so-called 'Later Mohist Canon' that document reflective thinking on epistemic and spatial concepts. The 'Later Mohist Canon' originated in late Warring States period China (ca. 300 BCE) and, among the corpus of extant, transmitted ancient Chinese texts, is highly atypical in several respects concerning both contents and style. Yet, it is shown that there are many passages that can be clearly related to other, more traditional, contemporaneous sources. The interpretations given aim at the reconstruction of historical forms of thinking and are informed by pertinent linguistic and textual analysis. Furthermore, general issues of interpretation, such as the problem of anachronistic understanding, are discussed by way of example.

Abstract

This study is a reconstruction of the life and work of the Scottish mathematician and physician Duncan Liddel (Aberdeen, 1561–1613). It deals with Liddel’s curriculum studiorum and academic career in northern protestant Germany (at the universities of Frankfurt/Oder, Rostock and Helmstedt); his participation in the debates of important intellectual circles such as that of Dudith-Sbardellati and Crato von Crafftheim in Wrocław and Tycho’s “astronomical Academy” on Hven, in Denmark; and Liddel’s eventual return to Aberdeen, where he funded a chair of mathematics and a scholarship for several students at the Marischal College and endowed the university with his scientific and humanistic library. This bio-bibliographical study, based on archival and library investigations, offers an insight into the institutions and networks that permitted a wide European circulation of scholars and ideas, as well as transfer processes of knowledge and scientific practices, during the Renaissance.

Abstract

In the context of a new analysis of the notebooks of Erwin Schrödinger, the paper deals with the question of the relation between Schrödinger's creation of wave mechanics and the contemporary efforts by Werner Heisenberg and his colleagues to establish a new quantum mechanics. How can one explain, from a broader historical and epistemological perspective, the astonishing simultaneity and complementarity of these discoveries? The paper argues that neither the physical problems with which both approaches deal nor what ultimately turned out to be their common mathematical ground are sufficient to explain their complementarity. Instead, their closeness is explained by analyzing their common roots in classical mechanics and its transformation in the light of the most fundamental new quantum law, the relation between energy and frequency found by Planck. It is shown, in particular, that for both approaches a bridge between quantum and classical aspects involving this relation was crucial. In the case of Heisenberg, this bridge was given by Bohr’s correspondence principle. In the case of Schrödinger it was constituted by Hamilton’s optical-mechanical analogy.

436

Jens Høyrup

A hypothetical history of Old Babylonian mathematics: places, passages, stages, development

Copernicus in the Cultural Debates of the
Renaissance: Reception, Legacy, Transformation [Part I & II]

2012

Abstract

This extensive study offers a general overview of the reception of Copernicus’s astronomical and cosmological proposal from the years immediately preceding the publication of his major work, De revolutionibus orbium coelestium (Nuremberg, 1543), to the Catholic prohibition of the heliocentric system in 1616. It is a reconstruction of the Renaissance cultural debates that were either provoked by the impact of Copernicus’s work or that conversely reshaped and transformed the meaning of Copernicus’s achievements. Certain aspects of this reception and transformation are treated with particular attention: epistemology, cosmology, space conceptions, natural philosophy, the incipient classical physics, theology and anthropology. The treatment of the different authors, issues and debates is based on an extensive and up-to-date bibliography concerning both the primary sources and the secondary literature.

428

Stefano Bordoni

Widening the Scope of Analytical Mechanics. Duhem’s third pathway to Thermodynamics

Abstract

The paper reviews the historical origins of the current split between different forms of reflection on science, in particular between normative philosophical positions and descriptive historical positions that consider science as embedded in society and culture. It analyzes the historical and intellectual contexts in which this split emerged in the early part of the twentieth century, taking the philosopher Moritz Schlick and the scientist and historian Ludwik Fleck as main reference points. The history of Einstein’s general theory of relativity and its new understanding of space and time is analyzed in relation to these positions. The paper follows the split between the different forms of reflection through further developments in the philosophy and history of science, discussing the views of Otto Neurath, Rudolf Carnap, Martin Heidegger, and Thomas Kuhn, among others. It suggests that current debates on historical epistemology could benefit from taking the split of rationality—inherited from the catastrophic twentieth century—as a challenge to be addressed by an integrative historical theory of knowledge development.

(1)Voltaire’s Newtonianism. A Bridge from English Empiricism to Cartesian Rationalism and Its Implications for the Concept of Mechanics in German Idealism (2) Christian Wolff’s Mechanical Philosophy: A Comparison with Isaac Newton’s Mechanics

(1) Scalpel or Rays? Radiotherapy and the Struggle for the Cancer Patient in Pre-World War II Germany
(2) A Dispute over Scientific Credibility: The Struggle for an Independent Institute for Cancer Research in Pre-World War II Berlin